SOLUTION: If a and b are positive real numbers and each of the equations {{{ x^2+ax+2b=0}}} and {{{x^2+2bx+a=0}}} has real roots, what is the smallest possible value of a+b?

SOLUTION: If a and b are positive real numbers and each of the equations {{{ x^2+ax+2b=0}}} and {{{x^2+2bx+a=0}}} has real roots, what is the smallest possible value of a+b?

Algebra.Com

Question 670823: If a and b are positive real numbers and each of the equations and has real roots, what is the smallest possible value of a+b?
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Using the quadratic formula on the first one we get:

Second:

Which when set equal to each other we get b = (a/2) and so b = 2 and a = 4
So a+b = 6

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